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Pressure change with constant volume

  1. Nov 23, 2013 #1
    1. The problem statement, all variables and given/known data
    Given two moles of some gas with two atoms per molecule which has energy [itex]U=aK_{B}T[/itex].
    Assume the initial pressure is [itex]P_{i}= 2[/itex] Atm and the initial volume is [itex]P_{i}= 0.001\ m^{3}[/itex].
    Now we heat it in an isochoric process to [itex]2P_{i}[/itex].

    What would be [itex]\Delta T[/itex]?
    What would be the work required to do that?
    What would be the change in the gas particles' internal energy?

    2. Relevant equations
    [itex]U=aK_{B}T[/itex]
    [itex]dU=PdS-TdV[/itex]

    3. The attempt at a solution
    Well using the first law of thermodynamics, I got that under constant volume [itex]dV=0[/itex] so [itex]\frac{dQ}{dT}=\frac{\partial U}{\partial T}[/itex] so the entire energy that we spent on heating would be transferred into the gas.
    What's a tricky to me is to formulate the change in temperature as a function of pressure because [itex]dV=0[/itex] so I'd really welcome a hint.

    Thanks!
     
    Last edited: Nov 23, 2013
  2. jcsd
  3. Nov 23, 2013 #2

    TSny

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    Oops, check that.

    Can you assume the gas obeys the ideal gas law?
     
  4. Nov 24, 2013 #3
    And yes of course it was a typo :) it's supposed to be [itex]dU=TdS-PdV[/itex]

    I'm really not sure whether I can, is there a way of solving this without this assumption?
     
    Last edited: Nov 24, 2013
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